signal op• Data kinds: signal → signal
• Call: import fullseye as fs; fs.ledger.companding_mu_law(x, mu=255.0, bits=8) (to call the implementation directly, import dsp; dsp.companding_mu_law(x, mu=255.0, bits=8); from the registry, ops1d.get("companding_mu_law"))
mu-law companding — the G.711 curve, used here on any 1-D signal.
Compress with `F(v) = sign(v) * ln(1 + mu|v|) / ln(1 + mu)` on the signal
scaled to `[-1, 1]`, quantise uniformly, expand back. The steps end up fine
near zero and coarse near full scale, which is the right allocation when the
interesting part of the signal is small compared with its peaks — speech,
vibration, anything with a large crest factor.
This is where mu-law comes from: the image operator
`companding_mu_law` is the same curve applied to intensity. Reporting both
keeps the family honest about which dimension the technique was designed for.
Applicability — it is the crest factor that decides. Measured on a sine
of amplitude *A* with one sample pinned at full scale, so the crest factor is
exactly `1/A` (mean square error relative to a uniform quantiser):
crest 50 4 bit 0.011 6 bit 0.014 (about 90x better)
crest 20 4 bit 0.122 6 bit 0.101
crest 6.7 4 bit 0.613 6 bit 0.616
crest 2.0 4 bit 4.22 6 bit 6.03 (several times WORSE)
So the rule is crest factor above roughly 7 — speech, vibration, impact.
Below that, a plain uniform quantiser wins and mu-law actively hurts.
★Note the peak is a single sample: on random signals of the same family
the advantage swung between 0.55 and 0.87 purely with the seed, because the
largest excursion sets the scale. Measure the crest factor of *your* signal,
do not assume it from the distribution.
Other limits: `mu` near 0 degenerates to uniform quantisation (that is how
you check the curve is doing anything), and the curve is fixed — unlike a
Lloyd-Max codebook fitted to the signal — which is the point when values must
stay comparable across recordings.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• gallery2d_gray_arith — py -3.11 examples/gallery2d_gray_arith.py
signal as input)create_funct_1d_array · create_funct_1d_pairs · smooth_funct_1d_gauss · smooth_funct_1d_mean · derivate_funct_1d · integrate_funct_1d · zero_crossings_funct_1d · local_min_max_funct_1d
signal)lowpass · highpass · bandpass · envelope · rms · local_std · quantize · resample
*Provenance: dsp.py — ONED operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.